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dynhpg.F90 in branches/2011/dev_NEMO_MERGE_2011/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/2011/dev_NEMO_MERGE_2011/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 3118

Last change on this file since 3118 was 3118, checked in by cetlod, 12 years ago
branch dev_NEMO_MERGE_2011/NEMOGCM: minor bug corrections
Property svn:keywords set to `Id`
File size: 52.6 KB

Line
1	MODULE dynhpg
2	!!======================================================================
3	!! * MODULE dynhpg *
4	!! Ocean dynamics: hydrostatic pressure gradient trend
5	!!======================================================================
6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
7	!! 5.0 ! 1991-11 (G. Madec)
8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
14	!! - ! 2005-11 (G. Madec) style & small optimisation
15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
16	!! 3.4 ! 2011-11 (A. Coward, H. Liu) introduction of prj scheme;
17	!! ! suppression of hel, wdj and rot options
18	!!----------------------------------------------------------------------
19
20	!!----------------------------------------------------------------------
21	!! dyn_hpg : update the momentum trend with the now horizontal
22	!! gradient of the hydrostatic pressure
23	!! dyn_hpg_init : initialisation and control of options
24	!! hpg_zco : z-coordinate scheme
25	!! hpg_zps : z-coordinate plus partial steps (interpolation)
26	!! hpg_sco : s-coordinate (standard jacobian formulation)
27	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
28	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
29	!!----------------------------------------------------------------------
30	USE oce ! ocean dynamics and tracers
31	USE dom_oce ! ocean space and time domain
32	USE phycst ! physical constants
33	USE trdmod ! ocean dynamics trends
34	USE trdmod_oce ! ocean variables trends
35	USE in_out_manager ! I/O manager
36	USE prtctl ! Print control
37	USE lbclnk ! lateral boundary condition
38	USE lib_mpp ! MPP library
39
40	IMPLICIT NONE
41	PRIVATE
42
43	PUBLIC dyn_hpg ! routine called by step module
44	PUBLIC dyn_hpg_init ! routine called by opa module
45
46	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
47	LOGICAL , PUBLIC :: ln_hpg_zco = .TRUE. !: z-coordinate - full steps
48	LOGICAL , PUBLIC :: ln_hpg_zps = .FALSE. !: z-coordinate - partial steps (interpolation)
49	LOGICAL , PUBLIC :: ln_hpg_sco = .FALSE. !: s-coordinate (standard jacobian formulation)
50	LOGICAL , PUBLIC :: ln_hpg_djc = .FALSE. !: s-coordinate (Density Jacobian with Cubic polynomial)
51	LOGICAL , PUBLIC :: ln_hpg_prj = .FALSE. !: s-coordinate (Pressure Jacobian scheme)
52	LOGICAL , PUBLIC :: ln_dynhpg_imp = .FALSE. !: semi-implicite hpg flag
53
54	INTEGER :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags)
55
56	!! * Substitutions
57	# include "domzgr_substitute.h90"
58	# include "vectopt_loop_substitute.h90"
59	!!----------------------------------------------------------------------
60	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
61	!! $Id$
62	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
63	!!----------------------------------------------------------------------
64	CONTAINS
65
66	SUBROUTINE dyn_hpg( kt )
67	!!---------------------------------------------------------------------
68	!! * ROUTINE dyn_hpg *
69	!!
70	!! ** Method : Call the hydrostatic pressure gradient routine
71	!! using the scheme defined in the namelist
72	!!
73	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
74	!! - Save the trend (l_trddyn=T)
75	!!----------------------------------------------------------------------
76	USE oce, ONLY: tsa ! (tsa) used as 2 3D workspace
77	!!
78	INTEGER, INTENT(in) :: kt ! ocean time-step index
79	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
80	!!----------------------------------------------------------------------
81	!
82	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
83	ztrdu => tsa(:,:,:,1)
84	ztrdv => tsa(:,:,:,2)
85	!
86	ztrdu(:,:,:) = ua(:,:,:)
87	ztrdv(:,:,:) = va(:,:,:)
88	ENDIF
89	!
90	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
91	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
92	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
93	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
94	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
95	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
96	END SELECT
97	!
98	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
99	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
100	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
101	CALL trd_mod( ztrdu, ztrdv, jpdyn_trd_hpg, 'DYN', kt )
102	ENDIF
103	!
104	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
105	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
106	!
107	END SUBROUTINE dyn_hpg
108
109
110	SUBROUTINE dyn_hpg_init
111	!!----------------------------------------------------------------------
112	!! * ROUTINE dyn_hpg_init *
113	!!
114	!! ** Purpose : initializations for the hydrostatic pressure gradient
115	!! computation and consistency control
116	!!
117	!! ** Action : Read the namelist namdyn_hpg and check the consistency
118	!! with the type of vertical coordinate used (zco, zps, sco)
119	!!----------------------------------------------------------------------
120	INTEGER :: ioptio = 0 ! temporary integer
121	!!
122	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
123	& ln_hpg_djc, ln_hpg_prj, ln_dynhpg_imp
124	!!----------------------------------------------------------------------
125	!
126	REWIND( numnam ) ! Read Namelist namdyn_hpg
127	READ ( numnam, namdyn_hpg )
128	!
129	IF(lwp) THEN ! Control print
130	WRITE(numout,*)
131	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
132	WRITE(numout,*) '~~~~~~~~~~~~'
133	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
134	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
135	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
136	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
137	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
138	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
139	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
140	ENDIF
141	!
142	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj) ) &
143	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
144	& the standard jacobian formulation hpg_sco or &
145	& the pressure jacobian formulation hpg_prj')
146	!
147	! ! Set nhpg from ln_hpg_... flags
148	IF( ln_hpg_zco ) nhpg = 0
149	IF( ln_hpg_zps ) nhpg = 1
150	IF( ln_hpg_sco ) nhpg = 2
151	IF( ln_hpg_djc ) nhpg = 3
152	IF( ln_hpg_prj ) nhpg = 4
153	!
154	! ! Consistency check
155	ioptio = 0
156	IF( ln_hpg_zco ) ioptio = ioptio + 1
157	IF( ln_hpg_zps ) ioptio = ioptio + 1
158	IF( ln_hpg_sco ) ioptio = ioptio + 1
159	IF( ln_hpg_djc ) ioptio = ioptio + 1
160	IF( ln_hpg_prj ) ioptio = ioptio + 1
161	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
162	!
163	END SUBROUTINE dyn_hpg_init
164
165
166	SUBROUTINE hpg_zco( kt )
167	!!---------------------------------------------------------------------
168	!! * ROUTINE hpg_zco *
169	!!
170	!! ** Method : z-coordinate case, levels are horizontal surfaces.
171	!! The now hydrostatic pressure gradient at a given level, jk,
172	!! is computed by taking the vertical integral of the in-situ
173	!! density gradient along the model level from the suface to that
174	!! level: zhpi = grav .....
175	!! zhpj = grav .....
176	!! add it to the general momentum trend (ua,va).
177	!! ua = ua - 1/e1u * zhpi
178	!! va = va - 1/e2v * zhpj
179	!!
180	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
181	!!----------------------------------------------------------------------
182	USE oce, ONLY: tsa ! (tsa) used as 2 3D workspace
183	!!
184	INTEGER, INTENT(in) :: kt ! ocean time-step index
185	!!
186	INTEGER :: ji, jj, jk ! dummy loop indices
187	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
188	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
189	!!----------------------------------------------------------------------
190
191	zhpi => tsa(:,:,:,1)
192	zhpj => tsa(:,:,:,2)
193	!
194	IF( kt == nit000 ) THEN
195	IF(lwp) WRITE(numout,*)
196	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
197	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
198	ENDIF
199
200	zcoef0 = - grav * 0.5_wp ! Local constant initialization
201
202	! Surface value
203	DO jj = 2, jpjm1
204	DO ji = fs_2, fs_jpim1 ! vector opt.
205	zcoef1 = zcoef0 * fse3w(ji,jj,1)
206	! hydrostatic pressure gradient
207	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
208	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
209	! add to the general momentum trend
210	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
211	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
212	END DO
213	END DO
214
215	!
216	! interior value (2=<jk=<jpkm1)
217	DO jk = 2, jpkm1
218	DO jj = 2, jpjm1
219	DO ji = fs_2, fs_jpim1 ! vector opt.
220	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
221	! hydrostatic pressure gradient
222	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
223	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
224	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
225
226	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
227	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
228	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
229	! add to the general momentum trend
230	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
231	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
232	END DO
233	END DO
234	END DO
235	!
236	END SUBROUTINE hpg_zco
237
238
239	SUBROUTINE hpg_zps( kt )
240	!!---------------------------------------------------------------------
241	!! * ROUTINE hpg_zps *
242	!!
243	!! ** Method : z-coordinate plus partial steps case. blahblah...
244	!!
245	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
246	!!----------------------------------------------------------------------
247	USE oce, ONLY: tsa ! (tsa) used as 2 3D workspace
248	!!
249	INTEGER, INTENT(in) :: kt ! ocean time-step index
250	!!
251	INTEGER :: ji, jj, jk ! dummy loop indices
252	INTEGER :: iku, ikv ! temporary integers
253	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
254	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
255	!!----------------------------------------------------------------------
256
257	zhpi => tsa(:,:,:,1)
258	zhpj => tsa(:,:,:,2)
259	!
260	IF( kt == nit000 ) THEN
261	IF(lwp) WRITE(numout,*)
262	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
263	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
264	ENDIF
265
266
267	! Local constant initialization
268	zcoef0 = - grav * 0.5_wp
269
270	! Surface value (also valid in partial step case)
271	DO jj = 2, jpjm1
272	DO ji = fs_2, fs_jpim1 ! vector opt.
273	zcoef1 = zcoef0 * fse3w(ji,jj,1)
274	! hydrostatic pressure gradient
275	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
276	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
277	! add to the general momentum trend
278	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
279	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
280	END DO
281	END DO
282
283
284	! interior value (2=<jk=<jpkm1)
285	DO jk = 2, jpkm1
286	DO jj = 2, jpjm1
287	DO ji = fs_2, fs_jpim1 ! vector opt.
288	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
289	! hydrostatic pressure gradient
290	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
291	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
292	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
293
294	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
295	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
296	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
297	! add to the general momentum trend
298	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
299	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
300	END DO
301	END DO
302	END DO
303
304
305	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
306	# if defined key_vectopt_loop
307	jj = 1
308	DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling)
309	# else
310	DO jj = 2, jpjm1
311	DO ji = 2, jpim1
312	# endif
313	iku = mbku(ji,jj)
314	ikv = mbkv(ji,jj)
315	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
316	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
317	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
318	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
319	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
320	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
321	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
322	ENDIF
323	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
324	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
325	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
326	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
327	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
328	ENDIF
329	# if ! defined key_vectopt_loop
330	END DO
331	# endif
332	END DO
333	!
334
335	END SUBROUTINE hpg_zps
336
337
338	SUBROUTINE hpg_sco( kt )
339	!!---------------------------------------------------------------------
340	!! * ROUTINE hpg_sco *
341	!!
342	!! ** Method : s-coordinate case. Jacobian scheme.
343	!! The now hydrostatic pressure gradient at a given level, jk,
344	!! is computed by taking the vertical integral of the in-situ
345	!! density gradient along the model level from the suface to that
346	!! level. s-coordinates (ln_sco): a corrective term is added
347	!! to the horizontal pressure gradient :
348	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
349	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
350	!! add it to the general momentum trend (ua,va).
351	!! ua = ua - 1/e1u * zhpi
352	!! va = va - 1/e2v * zhpj
353	!!
354	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
355	!!----------------------------------------------------------------------
356	USE oce, ONLY: tsa ! (tsa) used as 2 3D workspace
357	!!
358	INTEGER, INTENT(in) :: kt ! ocean time-step index
359	!!
360	INTEGER :: ji, jj, jk ! dummy loop indices
361	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
362	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
363	!!----------------------------------------------------------------------
364
365	zhpi => tsa(:,:,:,1)
366	zhpj => tsa(:,:,:,2)
367	!
368	IF( kt == nit000 ) THEN
369	IF(lwp) WRITE(numout,*)
370	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
371	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
372	ENDIF
373
374	! Local constant initialization
375	zcoef0 = - grav * 0.5_wp
376	! To use density and not density anomaly
377	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
378	ELSE ; znad = 0._wp ! Fixed volume
379	ENDIF
380
381	! Surface value
382	DO jj = 2, jpjm1
383	DO ji = fs_2, fs_jpim1 ! vector opt.
384	! hydrostatic pressure gradient along s-surfaces
385	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
386	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
387	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
388	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
389	! s-coordinate pressure gradient correction
390	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
391	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
392	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
393	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
394	! add to the general momentum trend
395	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
396	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
397	END DO
398	END DO
399
400	! interior value (2=<jk=<jpkm1)
401	DO jk = 2, jpkm1
402	DO jj = 2, jpjm1
403	DO ji = fs_2, fs_jpim1 ! vector opt.
404	! hydrostatic pressure gradient along s-surfaces
405	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
406	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
407	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
408	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
409	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
410	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
411	! s-coordinate pressure gradient correction
412	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
413	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
414	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
415	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
416	! add to the general momentum trend
417	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
418	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
419	END DO
420	END DO
421	END DO
422	!
423	END SUBROUTINE hpg_sco
424
425	SUBROUTINE hpg_djc( kt )
426	!!---------------------------------------------------------------------
427	!! * ROUTINE hpg_djc *
428	!!
429	!! ** Method : Density Jacobian with Cubic polynomial scheme
430	!!
431	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
432	!!----------------------------------------------------------------------
433	USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released
434	USE oce , ONLY: tsa ! (tsa) used as 2 3D workspace
435	USE wrk_nemo, ONLY: drhox => wrk_3d_1 , dzx => wrk_3d_2
436	USE wrk_nemo, ONLY: drhou => wrk_3d_3 , dzu => wrk_3d_4 , rho_i => wrk_3d_5
437	USE wrk_nemo, ONLY: drhoy => wrk_3d_6 , dzy => wrk_3d_7
438	USE wrk_nemo, ONLY: drhov => wrk_3d_8 , dzv => wrk_3d_9 , rho_j => wrk_3d_10
439	USE wrk_nemo, ONLY: drhoz => wrk_3d_11 , dzz => wrk_3d_12
440	USE wrk_nemo, ONLY: drhow => wrk_3d_13 , dzw => wrk_3d_14
441	USE wrk_nemo, ONLY: rho_k => wrk_3d_15
442	!!
443	INTEGER, INTENT(in) :: kt ! ocean time-step index
444	!!
445	INTEGER :: ji, jj, jk ! dummy loop indices
446	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
447	REAL(wp) :: z1_10, cffu, cffx ! " "
448	REAL(wp) :: z1_12, cffv, cffy ! " "
449	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
450	!!----------------------------------------------------------------------
451
452	IF( wrk_in_use(3, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) ) THEN
453	CALL ctl_stop('dyn:hpg_djc: requested workspace arrays unavailable') ; RETURN
454	ENDIF
455	!
456	zhpi => tsa(:,:,:,1)
457	zhpj => tsa(:,:,:,2)
458
459	IF( kt == nit000 ) THEN
460	IF(lwp) WRITE(numout,*)
461	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
462	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
463	ENDIF
464
465	! Local constant initialization
466	zcoef0 = - grav * 0.5_wp
467	z1_10 = 1._wp / 10._wp
468	z1_12 = 1._wp / 12._wp
469
470	!----------------------------------------------------------------------------------------
471	! compute and store in provisional arrays elementary vertical and horizontal differences
472	!----------------------------------------------------------------------------------------
473
474	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
475
476	DO jk = 2, jpkm1
477	DO jj = 2, jpjm1
478	DO ji = fs_2, fs_jpim1 ! vector opt.
479	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
480	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
481	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
482	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
483	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
484	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
485	END DO
486	END DO
487	END DO
488
489	!-------------------------------------------------------------------------
490	! compute harmonic averages using eq. 5.18
491	!-------------------------------------------------------------------------
492	zep = 1.e-15
493
494	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
495	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
496
497	DO jk = 2, jpkm1
498	DO jj = 2, jpjm1
499	DO ji = fs_2, fs_jpim1 ! vector opt.
500	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
501
502	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
503	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
504
505	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
506	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
507
508	IF( cffw > zep) THEN
509	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
510	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
511	ELSE
512	drhow(ji,jj,jk) = 0._wp
513	ENDIF
514
515	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
516	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
517
518	IF( cffu > zep ) THEN
519	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
520	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
521	ELSE
522	drhou(ji,jj,jk ) = 0._wp
523	ENDIF
524
525	IF( cffx > zep ) THEN
526	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
527	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
528	ELSE
529	dzu(ji,jj,jk) = 0._wp
530	ENDIF
531
532	IF( cffv > zep ) THEN
533	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
534	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
535	ELSE
536	drhov(ji,jj,jk) = 0._wp
537	ENDIF
538
539	IF( cffy > zep ) THEN
540	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
541	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
542	ELSE
543	dzv(ji,jj,jk) = 0._wp
544	ENDIF
545
546	END DO
547	END DO
548	END DO
549
550	!----------------------------------------------------------------------------------
551	! apply boundary conditions at top and bottom using 5.36-5.37
552	!----------------------------------------------------------------------------------
553	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
554	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
555	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
556
557	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
558	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
559	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
560
561
562	!--------------------------------------------------------------
563	! Upper half of top-most grid box, compute and store
564	!-------------------------------------------------------------
565
566	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
567	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
568
569	DO jj = 2, jpjm1
570	DO ji = fs_2, fs_jpim1 ! vector opt.
571	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
572	& * ( rhd(ji,jj,1) &
573	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
574	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
575	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
576	END DO
577	END DO
578
579	!!bug gm : here also, simplification is possible
580	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
581
582	DO jk = 2, jpkm1
583	DO jj = 2, jpjm1
584	DO ji = fs_2, fs_jpim1 ! vector opt.
585
586	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
587	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
588	& - grav * z1_10 * ( &
589	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
590	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
591	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
592	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
593	& )
594
595	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
596	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
597	& - grav* z1_10 * ( &
598	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
599	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
600	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
601	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
602	& )
603
604	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
605	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
606	& - grav* z1_10 * ( &
607	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
608	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
609	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
610	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
611	& )
612
613	END DO
614	END DO
615	END DO
616	CALL lbc_lnk(rho_k,'W',1.)
617	CALL lbc_lnk(rho_i,'U',1.)
618	CALL lbc_lnk(rho_j,'V',1.)
619
620
621	! ---------------
622	! Surface value
623	! ---------------
624	DO jj = 2, jpjm1
625	DO ji = fs_2, fs_jpim1 ! vector opt.
626	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
627	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
628	! add to the general momentum trend
629	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
630	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
631	END DO
632	END DO
633
634	! ----------------
635	! interior value (2=<jk=<jpkm1)
636	! ----------------
637	DO jk = 2, jpkm1
638	DO jj = 2, jpjm1
639	DO ji = fs_2, fs_jpim1 ! vector opt.
640	! hydrostatic pressure gradient along s-surfaces
641	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
642	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
643	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
644	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
645	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
646	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
647	! add to the general momentum trend
648	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
649	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
650	END DO
651	END DO
652	END DO
653	!
654	IF( wrk_not_released(3, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) ) &
655	CALL ctl_stop('dyn:hpg_djc: failed to release workspace arrays')
656	!
657	END SUBROUTINE hpg_djc
658
659
660	SUBROUTINE hpg_prj( kt )
661	!!---------------------------------------------------------------------
662	!! * ROUTINE hpg_prj *
663	!!
664	!! ** Method : s-coordinate case.
665	!! A Pressure-Jacobian horizontal pressure gradient method
666	!! based on the constrained cubic-spline interpolation for
667	!! all vertical coordinate systems
668	!!
669	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
670	!! - Save the trend (l_trddyn=T)
671	!!
672	!!----------------------------------------------------------------------
673
674	USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released
675	USE oce , ONLY: tsa ! (tsa) used as 2 3D workspace
676	USE wrk_nemo, ONLY: zhpi => wrk_3d_3
677	USE wrk_nemo, ONLY: zu => wrk_3d_4
678	USE wrk_nemo, ONLY: zv => wrk_3d_5
679	USE wrk_nemo, ONLY: fsp => wrk_3d_6
680	USE wrk_nemo, ONLY: xsp => wrk_3d_7
681	USE wrk_nemo, ONLY: asp => wrk_3d_8
682	USE wrk_nemo, ONLY: bsp => wrk_3d_9
683	USE wrk_nemo, ONLY: csp => wrk_3d_10
684	USE wrk_nemo, ONLY: dsp => wrk_3d_11
685	!!
686	!!----------------------------------------------------------------------
687	!!
688	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
689	INTEGER, INTENT(in) :: kt ! ocean time-step index
690	!!
691	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
692	REAL(wp) :: zcoef0, znad ! temporary scalars
693	!!
694	!! The local variables for the correction term
695	INTEGER :: jk1, jis, jid, jjs, jjd
696	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
697	REAL(wp) :: zrhdt1
698	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
699	INTEGER :: zbhitwe, zbhitns
700	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdeptht, zrhh
701	!!----------------------------------------------------------------------
702
703	IF( wrk_in_use(3, 3,4,5,6,7,8,9,10,11) ) THEN
704	CALL ctl_stop('dyn:hpg_prj: requested workspace arrays unavailable') ; RETURN
705	ENDIF
706	!
707	zdeptht => tsa(:,:,:,1)
708	zrhh => tsa(:,:,:,2)
709
710	IF( kt == nit000 ) THEN
711	IF(lwp) WRITE(numout,*)
712	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
713	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
714	ENDIF
715
716	!!----------------------------------------------------------------------
717	! Local constant initialization
718	zcoef0 = - grav
719	znad = 0.0_wp
720	IF( lk_vvl ) znad = 1._wp
721
722	! Clean 3-D work arrays
723	zhpi(:,:,:) = 0._wp
724	zrhh(:,:,:) = rhd(:,:,:)
725
726	! Preparing vertical density profile for hybrid-sco coordinate
727	DO jj = 1, jpj
728	DO ji = 1, jpi
729	jk = mbathy(ji,jj)
730	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
731	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
732	ELSE IF(jk < jpkm1) THEN
733	DO jkk = jk+1, jpk
734	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
735	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
736	END DO
737	ENDIF
738	END DO
739	END DO
740
741	DO jj = 1, jpj
742	DO ji = 1, jpi
743	zdeptht(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1)
744	zdeptht(ji,jj,1) = zdeptht(ji,jj,1) - sshn(ji,jj) * znad
745	DO jk = 2, jpk
746	zdeptht(ji,jj,jk) = zdeptht(ji,jj,jk-1) + fse3w(ji,jj,jk)
747	END DO
748	END DO
749	END DO
750
751	DO jk = 1, jpkm1
752	DO jj = 1, jpj
753	DO ji = 1, jpi
754	fsp(ji,jj,jk) = zrhh(ji,jj,jk)
755	xsp(ji,jj,jk) = zdeptht(ji,jj,jk)
756	END DO
757	END DO
758	END DO
759
760	! Construct the vertical density profile with the
761	! constrained cubic spline interpolation
762	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
763
764	! Calculate the hydrostatic pressure at T(ji,jj,1)
765	DO jj = 2, jpj
766	DO ji = 2, jpi
767	zrhdt1 = zrhh(ji,jj,1) - interp3(zdeptht(ji,jj,1),asp(ji,jj,1), &
768	bsp(ji,jj,1), csp(ji,jj,1), &
769	dsp(ji,jj,1) ) * 0.5_wp * zdeptht(ji,jj,1)
770	zrhdt1 = MAX(zrhdt1, 1000._wp - rau0) ! no lighter than fresh water
771
772	! assuming linear profile across the top half surface layer
773	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
774	END DO
775	END DO
776
777	! Calculate the pressure at T(ji,jj,2:jpkm1)
778	DO jk = 2, jpkm1
779	DO jj = 2, jpj
780	DO ji = 2, jpi
781	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
782	integ2(zdeptht(ji,jj,jk-1), zdeptht(ji,jj,jk),&
783	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
784	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
785	END DO
786	END DO
787	END DO
788
789	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
790	DO jj = 2, jpjm1
791	DO ji = 2, jpim1
792	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - sshu_n(ji,jj) * znad)
793	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - sshv_n(ji,jj) * znad)
794	END DO
795	END DO
796
797	DO jk = 2, jpkm1
798	DO jj = 2, jpjm1
799	DO ji = 2, jpim1
800	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
801	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
802	END DO
803	END DO
804	END DO
805
806	DO jk = 1, jpkm1
807	DO jj = 2, jpjm1
808	DO ji = 2, jpim1
809	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
810	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
811	END DO
812	END DO
813	END DO
814
815	DO jk = 1, jpkm1
816	DO jj = 2, jpjm1
817	DO ji = 2, jpim1
818	zpwes = 0._wp; zpwed = 0._wp
819	zpnss = 0._wp; zpnsd = 0._wp
820	zuijk = zu(ji,jj,jk)
821	zvijk = zv(ji,jj,jk)
822
823	!!!!! for u equation
824	IF( jk <= mbku(ji,jj) ) THEN
825	IF( -zdeptht(ji+1,jj,mbku(ji,jj)) >= -zdeptht(ji,jj,mbku(ji,jj)) ) THEN
826	jis = ji + 1; jid = ji
827	ELSE
828	jis = ji; jid = ji +1
829	ENDIF
830
831	! integrate the pressure on the shallow side
832	jk1 = jk
833	zbhitwe = 0
834	DO WHILE ( -zdeptht(jis,jj,jk1) > zuijk )
835	IF( jk1 == mbku(ji,jj) ) THEN
836	zbhitwe = 1
837	EXIT
838	ENDIF
839	zdeps = MIN(zdeptht(jis,jj,jk1+1), -zuijk)
840	zpwes = zpwes + &
841	integ2(zdeptht(jis,jj,jk1), zdeps, &
842	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
843	csp(jis,jj,jk1), dsp(jis,jj,jk1))
844	jk1 = jk1 + 1
845	END DO
846
847	IF(zbhitwe == 1) THEN
848	zuijk = -zdeptht(jis,jj,jk1)
849	ENDIF
850
851	! integrate the pressure on the deep side
852	jk1 = jk
853	zbhitwe = 0
854	DO WHILE ( -zdeptht(jid,jj,jk1) < zuijk )
855	IF( jk1 == 1 ) THEN
856	zbhitwe = 1
857	EXIT
858	ENDIF
859	zdeps = MAX(zdeptht(jid,jj,jk1-1), -zuijk)
860	zpwed = zpwed + &
861	integ2(zdeps, zdeptht(jid,jj,jk1), &
862	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
863	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
864	jk1 = jk1 - 1
865	END DO
866
867	IF( zbhitwe == 1 ) THEN
868	zdeps = zdeptht(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
869	zrhdt1 = zrhh(jid,jj,1) - interp3(zdeptht(jid,jj,1), asp(jid,jj,1), &
870	bsp(jid,jj,1), csp(jid,jj,1), &
871	dsp(jid,jj,1)) * zdeps
872	zrhdt1 = MAX(zrhdt1, 1000._wp - rau0) ! no lighter than fresh water
873	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
874	ENDIF
875
876	! update the momentum trends in u direction
877
878	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
879	IF( lk_vvl ) THEN
880	zdpdx2 = zcoef0 / e1u(ji,jj) * &
881	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
882	ELSE
883	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
884	ENDIF
885
886	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
887	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
888	ENDIF
889
890	!!!!! for v equation
891	IF( jk <= mbkv(ji,jj) ) THEN
892	IF( -zdeptht(ji,jj+1,mbkv(ji,jj)) >= -zdeptht(ji,jj,mbkv(ji,jj)) ) THEN
893	jjs = jj + 1; jjd = jj
894	ELSE
895	jjs = jj ; jjd = jj + 1
896	ENDIF
897
898	! integrate the pressure on the shallow side
899	jk1 = jk
900	zbhitns = 0
901	DO WHILE ( -zdeptht(ji,jjs,jk1) > zvijk )
902	IF( jk1 == mbkv(ji,jj) ) THEN
903	zbhitns = 1
904	EXIT
905	ENDIF
906	zdeps = MIN(zdeptht(ji,jjs,jk1+1), -zvijk)
907	zpnss = zpnss + &
908	integ2(zdeptht(ji,jjs,jk1), zdeps, &
909	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
910	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
911	jk1 = jk1 + 1
912	END DO
913
914	IF(zbhitns == 1) THEN
915	zvijk = -zdeptht(ji,jjs,jk1)
916	ENDIF
917
918	! integrate the pressure on the deep side
919	jk1 = jk
920	zbhitns = 0
921	DO WHILE ( -zdeptht(ji,jjd,jk1) < zvijk )
922	IF( jk1 == 1 ) THEN
923	zbhitns = 1
924	EXIT
925	ENDIF
926	zdeps = MAX(zdeptht(ji,jjd,jk1-1), -zvijk)
927	zpnsd = zpnsd + &
928	integ2(zdeps, zdeptht(ji,jjd,jk1), &
929	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
930	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
931	jk1 = jk1 - 1
932	END DO
933
934	IF( zbhitns == 1 ) THEN
935	zdeps = zdeptht(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
936	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdeptht(ji,jjd,1), asp(ji,jjd,1), &
937	bsp(ji,jjd,1), csp(ji,jjd,1), &
938	dsp(ji,jjd,1) ) * zdeps
939	zrhdt1 = MAX(zrhdt1, 1000._wp - rau0) ! no lighter than fresh water
940	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
941	ENDIF
942
943	! update the momentum trends in v direction
944
945	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
946	IF( lk_vvl ) THEN
947	zdpdy2 = zcoef0 / e2v(ji,jj) * &
948	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
949	ELSE
950	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
951	ENDIF
952
953	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
954	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
955	ENDIF
956
957
958	END DO
959	END DO
960	END DO
961
962	!
963	IF( wrk_not_released(3, 3,4,5,6,7,8,9,10,11) ) &
964	CALL ctl_stop('dyn:hpg_prj: failed to release workspace arrays')
965	!
966	END SUBROUTINE hpg_prj
967
968	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
969	!!----------------------------------------------------------------------
970	!! * ROUTINE cspline *
971	!!
972	!! ** Purpose : constrained cubic spline interpolation
973	!!
974	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
975	!! Reference: K.W. Brodlie, A review of mehtods for curve and function
976	!! drawing, 1980
977	!!
978	!!----------------------------------------------------------------------
979	IMPLICIT NONE
980	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
981	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
982	! the interpoated function
983	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
984	! 2: Linear
985
986	! Local Variables
987	INTEGER :: ji, jj, jk ! dummy loop indices
988	INTEGER :: jpi, jpj, jpkm1
989	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
990	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
991	REAL(wp) :: zdf(size(fsp,3))
992	!!----------------------------------------------------------------------
993
994	jpi = size(fsp,1)
995	jpj = size(fsp,2)
996	jpkm1 = size(fsp,3) - 1
997
998	! Clean output arrays
999	asp = 0.0_wp
1000	bsp = 0.0_wp
1001	csp = 0.0_wp
1002	dsp = 0.0_wp
1003
1004	DO ji = 1, jpi
1005	DO jj = 1, jpj
1006	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1007	DO jk = 2, jpkm1-1
1008	zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1009	zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1010	zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1011	zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1012
1013	zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1014
1015	IF(zdf1 * zdf2 <= 0._wp) THEN
1016	zdf(jk) = 0._wp
1017	ELSE
1018	zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1019	ENDIF
1020	END DO
1021
1022	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1023	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1024	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1025	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
1026	& 0.5_wp * zdf(jpkm1 - 1)
1027
1028	DO jk = 1, jpkm1 - 1
1029	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1030	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1031	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1032	zddf1 = -2._wp * ztmp1 + ztmp2
1033	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1034	zddf2 = 2._wp * ztmp1 - ztmp2
1035
1036	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1037	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1038	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1039	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1040	& dsp(ji,jj,jk) * ( xsp(ji,jj,jk+1)**2 + &
1041	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk) + &
1042	& xsp(ji,jj,jk)**2 )
1043	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) - &
1044	& csp(ji,jj,jk) * xsp(ji,jj,jk)**2 - &
1045	& dsp(ji,jj,jk) * xsp(ji,jj,jk)**3
1046	END DO
1047
1048	ELSE IF (polynomial_type == 2) THEN ! Linear
1049
1050	DO jk = 1, jpkm1-1
1051	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1052	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1053
1054	dsp(ji,jj,jk) = 0._wp
1055	csp(ji,jj,jk) = 0._wp
1056	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1057	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1058	END DO
1059
1060	ELSE
1061	CALL ctl_stop( 'invalid polynomial type in cspline' )
1062	ENDIF
1063
1064	END DO
1065	END DO
1066
1067	END SUBROUTINE cspline
1068
1069
1070	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1071	!!----------------------------------------------------------------------
1072	!! * ROUTINE interp1 *
1073	!!
1074	!! ** Purpose : 1-d linear interpolation
1075	!!
1076	!! ** Method :
1077	!! interpolation is straight forward
1078	!! extrapolation is also permitted (no value limit)
1079	!!
1080	!! H.Liu, Jan 2009, POL
1081	!!----------------------------------------------------------------------
1082	IMPLICIT NONE
1083	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1084	REAL(wp) :: f ! result of the interpolation (extrapolation)
1085	REAL(wp) :: zdeltx
1086	!!----------------------------------------------------------------------
1087
1088	zdeltx = xr - xl
1089	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
1090	f = 0.5_wp * (fl + fr)
1091	ELSE
1092	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1093	ENDIF
1094
1095	END FUNCTION interp1
1096
1097	FUNCTION interp2(x, a, b, c, d) RESULT(f)
1098	!!----------------------------------------------------------------------
1099	!! * ROUTINE interp1 *
1100	!!
1101	!! ** Purpose : 1-d constrained cubic spline interpolation
1102	!!
1103	!! ** Method : cubic spline interpolation
1104	!!
1105	!!----------------------------------------------------------------------
1106	IMPLICIT NONE
1107	REAL(wp), INTENT(in) :: x, a, b, c, d
1108	REAL(wp) :: f ! value from the interpolation
1109	!!----------------------------------------------------------------------
1110
1111	f = a + x* ( b + x * ( c + d * x ) )
1112
1113	END FUNCTION interp2
1114
1115
1116	FUNCTION interp3(x, a, b, c, d) RESULT(f)
1117	!!----------------------------------------------------------------------
1118	!! * ROUTINE interp1 *
1119	!!
1120	!! ** Purpose : Calculate the first order of deriavtive of
1121	!! a cubic spline function y=a+bx+cx^2+d*x^3
1122	!!
1123	!! ** Method : f=dy/dx=b+2cx+3dx^2
1124	!!
1125	!!----------------------------------------------------------------------
1126	IMPLICIT NONE
1127	REAL(wp), INTENT(in) :: x, a, b, c, d
1128	REAL(wp) :: f ! value from the interpolation
1129	!!----------------------------------------------------------------------
1130
1131	f = b + x * ( 2._wp * c + 3._wp * d * x)
1132
1133	END FUNCTION interp3
1134
1135
1136	FUNCTION integ2(xl, xr, a, b, c, d) RESULT(f)
1137	!!----------------------------------------------------------------------
1138	!! * ROUTINE interp1 *
1139	!!
1140	!! ** Purpose : 1-d constrained cubic spline integration
1141	!!
1142	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1143	!!
1144	!!----------------------------------------------------------------------
1145	IMPLICIT NONE
1146	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1147	REAL(wp) :: za1, za2, za3
1148	REAL(wp) :: f ! integration result
1149	!!----------------------------------------------------------------------
1150
1151	za1 = 0.5_wp * b
1152	za2 = c / 3.0_wp
1153	za3 = 0.25_wp * d
1154
1155	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1156	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1157
1158	END FUNCTION integ2
1159
1160
1161	!!======================================================================
1162	END MODULE dynhpg

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